Question

Local government is worried that runoff from a corporate farm has caused water in a nearby stream to become acidic. The pH is used to measure the acidity/alkalinity of a substance. Pure water, for instance, has a pH of 7, and smaller pH values indicate acidity, while larger values indicate alkalinity. A contractor is hired to test the hypothesis that the water is significantly acidic.

H0: μ = 7
HA: μ < 7
The contractor took 27 water samples and found an average pH of 6.3 with a sample standard deviation of 1.86.
What is the test statistic for this sample? Give your answer to 2 decimal places.

Answer 1

`t=(6.3-7)/((1.86)/(√(27)))=-1.96`

Explanation:

Data given and notation

`\bar X=6.3` represent the sample mean

`s=1.86` represent the sample standard deviation

`n=27` sample size

`\mu_o =7` represent the value that we want to test

`\alpha` represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

`p_v` represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean iss lower than 7 or no, the system of hypothesis would be:

Null hypothesis:
`\mu \geq 7`

Alternative hypothesis:
`\mu < 7`

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

`t=(\bar X-\mu_o)/((s)/(√(n)))` (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

`t=(6.3-7)/((1.86)/(√(27)))=-1.96`